from lib_misc import gcd


def is_curious(n, d):
    assert(len(str(n)) == 2 and len(str(d)) == 2)
    if n == d:
        return False
    for i in range(1, 10):
        if str(i) in str(n) and str(i) in str(d):
            try:
                n_ = int(str(n).replace(str(i), ""))
                d_ = int(str(d).replace(str(i), ""))
            except ValueError:
                return False
            try:
                if n_ / d_ == n / d:
                    return True
            except ZeroDivisionError:
                return False
    return False


def euler_033():
    fs = [(n, d) for n in range(10, 100)
          for d in range(n, 100) if is_curious(n, d)]
    n = 1
    d = 1
    for n_, d_ in fs:
        n *= n_
        d *= d_
    return d // gcd(n, d)


if __name__ == "__main__":
    assert(is_curious(49, 98) is True)
    assert(is_curious(30, 50) is False)
    print("e033.py: {}".format(euler_033()))
    assert(euler_033() == 100)